Subgroups — C₂₃×#2103 #15669722

Order 2944.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#430	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#344	C₂	1	2	yes	maximal
4	C₂₃×#341	C₂	1	2	yes	maximal
5	C₂₃×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂×M₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#117	C₂²	1	1	yes	characteristic
11	C₂₃×#108	—	2	2	no	—
12	C₂₃×C₄⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₃	—	2	2	no	—
15	M₁₆×C₂₃	—	2	2	no	—
16	M₁₆×C₂₃	—	2	2	no	—
17	M₁₆×C₂₃	—	2	2	no	—
18	M₁₆×C₂₃	—	2	2	no	—
19	C₂×C₈×C₂₃	—	2	1	no	—
20	C₂×C₈×C₂₃	—	2	2	no	—
21	C₂×C₈×C₂₃	—	2	2	no	—
22	C₂×C₈×C₂₃	—	2	2	no	—
23	C₂×C₈×C₂₃	D₄	1	2	yes	—
24	C₄⋊C₄×C₂₃	—	2	1	no	—
25	C₂²⋊C₄×C₂₃	Q₈	1	2	yes	—
26	C₄²×C₂₃	—	2	1	no	—
27	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₂₃	—	2	2	no	—
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₃	#41	1	2	yes	—
31	C₂×C₄×C₂₃	#41	1	2	yes	—
32	C₂×C₄×C₂₃	#41	1	1	yes	characteristic
33	C₈×C₂₃	—	2	2	no	—
34	C₈×C₂₃	—	4	1	no	—
35	C₈×C₂₃	—	4	2	no	—
36	C₈×C₂₃	—	4	2	no	—
37	#2103	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₂₃	—	4	1	no	—
39	C₂²×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂²×C₂₃	#125	1	2	yes	—
41	C₄×C₂₃	—	4	2	no	—
42	C₄×C₂₃	#123	1	1	yes	characteristic
43	C₄×C₂₃	#124	1	1	yes	characteristic
44	C₄×C₂₃	#126	1	2	yes	—
45	#430	C₂×C₂₃	1	1	yes	characteristic
46	#424	C₂×C₂₃	1	1	yes	characteristic
47	#344	C₂×C₂₃	1	2	yes	—
48	#341	C₂×C₂₃	1	2	yes	—
49	#338	C₂×C₂₃	1	1	yes	characteristic
50	C₂×C₂₃	—	2	1	no	—
51	C₂×C₂₃	—	2	2	no	—
52	C₂×C₂₃	#400	1	1	yes	characteristic
53	C₂×M₁₆	C₂²×C₂₃	1	2	yes	—
54	C₂×M₁₆	C₂²×C₂₃	1	2	yes	—
55	C₂×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
56	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
57	#117	C₂²×C₂₃	1	1	yes	characteristic
58	#108	—	2	2	no	—
59	C₄⋊C₈	—	2	2	no	—
60	C₂₃	#2103	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	2	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	D₄×C₂₃	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Q₈×C₂₃	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Q₈×C₂₃	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
78	C₂×C₄	#41×C₂₃	1	2	yes	—
79	C₂×C₄	#41×C₂₃	1	2	yes	—
80	C₂×C₄	#41×C₂₃	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	4	2	no	—
84	C₈	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
87	C₂²	C₂₃×#125	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	C₂₃×#123	1	1	yes	characteristic
90	C₄	C₂₃×#124	1	1	yes	characteristic
91	C₄	C₂₃×#126	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	C₂₃×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#400
prime radical	C₂³×C₂₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
37. #2103	C₂₃	direct (N × H)
60. C₂₃	#2103	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#430	2
C₂₃×#424	2
C₂₃×#344	2
C₂₃×#341	2
C₂₃×#338	2
#2103	23

Subgroups — C23×#2103 #15669722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2103 #15669722